SOLUTION: Find the lateral area and the total area of the regular square base pyramid with an altitude of 24 and a slant height of 25.

Algebra ->  Surface-area -> SOLUTION: Find the lateral area and the total area of the regular square base pyramid with an altitude of 24 and a slant height of 25.      Log On


   

Question 1078574: Find the lateral area and the total area of the regular square base pyramid with an altitude of 24 and a slant height of 25.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The lateral area and total area would require knowing the size of that square base.
The problem does not provide that information directly,
but the length, s , of the base sides
can be calculated from the information given.
A top view, and a cross section of the pyramid
(cutting across the middle of opposite lateral faces)
would look like square and the isosceles triangle below
Applying the Pythagorean theorem to right triangle ABC,
%28s%2F2%29%5E2%2B24%5E2=25%5E2 --> %28s%2F2%29%5E2%2B576=625 --> %28s%2F2%29%5E2=625-576 --> %28s%2F2%29%5E2=49 --> s%2F2=7 --> s=14 .
The 4 lateral faces are triangles with base s=14 and height 25 ,
so the lateral area is
4%2A%2814%2A25%2F2%29=highlight%28700%29 square units
(of whatever units was used to measure pyramid height and slant height).
The area of the square base is 14%5E2=196 square units,
so the total area (in square units) is
700%2B196=highlight%28896%29 square units.